79 citations · 201 across the 42 of their papers we have counts for
51 papers
The Absolute Twistor Line and the Geometry of
Alain Connes, Caterina Consani
We construct the absolute algebraic geometry of the compactification by amalgamating the affine absolute curve $(\text{Spec}\, \mathbf Z)_{\mat…
On the Absolute Geometry of
Alain Connes, Caterina Consani
A guiding principle in P. Scholze's -adic geometry asserts that the points of over an algebraically closed perfectoid field of characteristic …
On the Jacobian of
Alain Connes, Caterina Consani
We interpret the structure of the adele class space of the rationals--and specifically its Riemann sector--as the natural monoidal extension of the Picard group of the arithmetic c…
Zeta Spectral Triples
Alain Connes, Caterina Consani, Henri Moscovici
We propose and investigate a strategy toward a proof of the Riemann Hypothesis based on a spectral realization of its non-trivial zeros. Our approach constructs self-adjoint operat…
Knots, primes and class field theory
Alain Connes, Caterina Consani
In this paper, we present a geometric generalization of class field theory, demonstrating how adelic constructions, central to the spectral realization of zeros of L-functions and…
On q-series and the moment problem associated to local factors
Alain Connes, Caterina Consani, Henri Moscovici
We investigate the moment problem and Jacobi matrix associated -- by the operator theoretic framework of the semilocal trace formula -- to each finite set of places of $\mathbb…